Duncan Foley On Why General Equilibrium Maybe Is Not Neoclassical Economics

Duncan Foley participated in a 2003 conference comparing and contrasting general equilibrium theory with long period models developed by advocates of the Cambridge capital critique. This is from the wrap-up discussion on the last day.

"I am in a somewhat peculiar position because due to certain idiosyncrasies of my education I never learned 'neoclassical economics'. The economic theory that I learned wasfrom Herbert Scarf and it was couched entirely in terms of the abstract general equilibrium model with n commodities, abstract production sets, and so forth. Someone has defined economic intuition as what you learn in your first course in economics, and since I did not learn the same things as many other people, my intuition is not the same. My economic intuition was always that there were no theorems of the following kind: suppose you increase the supply of labour, as a result the equilibrium real wage will fall. I knew there were no such theorems available in general equilibrium theory. I also knew, and maybe this became clearer because of Scarf's mathematical point of view, that once you took the step to a simultaneous general equilibrium vision, you had to give up hope of sustaining some traditional ideas. For one thing, you lost any sense of causality. In a general equilibrium model there is no real sense in which one factor causes another: everything is determined simultaneously by the whole collection of relationships... And I never thought there was any hope of proving general stability theorems, because Herbert Scarf had showed that you could not prove stability, at least tatonnement stability, without unacceptably strong hypotheses on aggregate demand functions. So these things are not counterintuitive to me, these are just facts of the matter. I see them as inherent defects of the general equilibrium point of view. I tend to read this as a case where neoclassical economics, in an attempt to purify itself logically, leached out all of the substance, the concrete substance and content, of what it had to say about the world. And it raises the question in my mind whether it is really fair to talk about general equilibrium theory as if it were neoclassical economics, precisely because it does not have that content of substitutability, well-behaved stability properties and well-behaved comparative statics properties. In fact, when I was at MIT it became apparent to me that for, say, Solow and Samuelson, who are perhaps closest to being true believers in the old neoclassical rules, general equilibrium theory was just as much a threat as the Cambridge controversy to their point of view." -- Duncan Foley (2003) final discussion, in: General Equilibirum: Problems and Propsoects (ed. by Fabio Petro and Frank Hahn), London: Routledge.

I have not looked at the American Economic Review, for example, in quite some time. But I have long lost an ability to make sense of mainstream economics. Doubtless, market power of employers, search costs for employees in finding new jobs, montoring costs and principal agent problems for employers, and the suggestion that an employee is a 'lemon' if they offer to work for a lower wage than many are all of empirical importance. But why must they be invoked to explain persistent unemployment or the failure of a rise in the minimum wage to create disemployment? The rigorous theory, in both the comparison of intertemporal general equilibrium paths and in comparisons of long period positions does not yield downward-sloping demand functions for labor. Likewise, rigorous theory does not yield regular supply and demand relations for other markets either.

Do mainstream economists even have an articulated, overall vision for microeconomics? Neither general equilibrium theory or game theory seem to provide one. Is it sufficient to just have lots of little models? This seems to be the position of mainstream economics for decades.

Gunnar Myrdal Sounding Like Tony Lawson?

This passage suggests to me that, in economics, one cannot expect to find event regularities from surface level data:

"The really important difference between us and our natural science colleagues is illustrated by the fact that we never reach down to constants like the speed of light and of sound in a particular medium, or the specific weights of atoms and molecules. We have nothing corresponding to the universally valid measurements of energy, voltage, amperes, and so on. The regularities we find do not have the firm, general, and lasting validity of 'laws of nature.'

If we economists, for instance, establish by observation the income or price elasticity for, say, sugar, our findings are valid for only a specific group of consumers in a single community or region at a particular time - not to mention the fact that the concept elasticity itself loses what I call adequacy to reality, and thereby analytical usefulness, in underdeveloped countries that have no, or very imperfect, 'markets,' in the sense given to this term by the economists." -- Gunnar Myrdal, Against the Stream: 138-139.

Myrdal wrote a lot about methodology. He was intererested in how unacknowledged valuations enter into economic theory. And he thinks social scientists should explicitly state their valuations. But he does not write about ontology.

I don't know how this applies to me. I suppose you can say that my focus on distribution, especially wages, reflects some valuations. I think, though, that I am mostly focusing on mathematics. And by looking for structures in parameter spaces for open models of prices of production, I am not making claims about event regularities at surface levels. I leave to others to relate movements in market prices to prices of production. Really, though, when I first learned about Robinson and Sraffa, I was astonished that a serious reason exists to think intermediate microeconomics, as widely taught, is nonsense, not even wrong.

Why Is Marginalist Economics Wrong?

Because of its treatment of capital. Other answers are possible.

This post draws heavily on the work of Pierangelo Garegnani. I start with a (parochial) definition of economics:

"Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses." -- Lionel Robbins (1932)

The scarce means are the factors of production: land, labor, and capital. Land and labor are in physical terms, in units of acres and person-years, respectively. They can be aggregated or disaggregated, as you wish.

But what is capital? Some early marginalists, such as Knut Wicksell took it as a value quantity, in units of dollars or pounds sterling. Maybe I should rather say, it is given in numeraire units. Capital is taken as given in quantity, but variable in form. The form is a matter of the specific quantities of specific plants, semi-finished goods, and so on.

The goal of the developers of this theory was to explain what Alfred Marshall called normal prices, in long period positions. This theory is inconsistent. As the economy approaches an equilibrium, prices change. The quantity of capital cannot be given a priori. It is both outside and inside the theory.

Leon Walras had a different approach. He took as given the quantities of the specific capital goods. He also included a commodity, perpetual net income, in his model. This is a kind of bond, what households who save may want to buy.

In a normal position, a uniform rate of return is made on all capital goods. Walras also had supply and demand matching. The model of capital formation is overdetermined and inconsistent. Furthermore, not all capital goods may be reproduced in Walras' model. (What did William Jaffe and Donald Walker think of this reading?)

In the 1930s and 1940s, certain marginalists, particularly Erik Lindahl, F. A. Hayek and J. R. Hicks, dropped the concept of a long-period equilibrium. They no longer required a uniform rate of profits in their model. The future is foreseen in their equilibrium paths. If a disequilibrium occurs, no reason exists for the economy to approach the previous path. Expectations and plans are inconsistent. An equilibrium path consistent with the initial data has no claim on our attention.

I am skipping over lots of variations on these themes. I do not even explain why, generally, the interest rate, in equilibrium, is not equal to the marginal product of capital. Or point out any empirical evidence for this result.

A modernized classical political economy, with affinities with Marx, provides a superior approach.

Selected References

• Barnett, Willam A. and Running Han. 2025. Economic Bifurcation and Chaos. World Scientific Publishing. [I have not read this]
• Dorfman, Robert, Paul Samuelson, Robert Solow. 1958. Linear Programming and Economic Analysis.
• Gram, Harvey and G. C. Harcourt. 2020. Keynesian uncertainty: the great divide between Joan Robinson and Paul Samuelson in their correspondence and public exchanges.
• Rosser, J. Barkley. 2013. From Catastrophe to Chaos: A General Theory of Economic Discontinuities, 2nd edition.
• Shell, Karl (ed.) 1967. Essays on the Theory of Optimal Economic Growth. MIT Press.

Givens For Two Approaches To The Theory Of Value And Distribution

1.0 Introduction

Broadly speaking, the history of political economy contains two approaches to value and distribution. For purposes of this post, I do not distinguish between classical and Marx's political economy. Institutionalists and those who know about German historical schools, for example, might have a complaint about being ignored.

This post is quite unoriginal. I thought I would just record these properties of two approaches.

2.0 Marginalism

Marginalist economics is about the allocation of given resources among alternatives. In marginalism, the theory of value and distribution is almost co-extensive with economic theory. The givens, for the theory of value and distribution, are:

• Endowments, including distribution of endowments among households.
• Tastes or preferences of each agent.
• Technology.

How to take capital as a given endowment is a difficulty with this approach. It can hardly be taken as a given quantity of value. The theory is supposed to explain prices, including the prices of capital goods. This problem is not just with aggregate theory. It is also a problem with microeconomic theory.

Another approach is to take initial quantities of individual capital goods as given. The neo-walrasian approach abandons the long run and the equalization of the rate of profits among industries. Conceptually, some expectations and plans must have been mistaken before the initial point in time. Yet the theory does not seem to accomodate such mistakes at the given time or into the future. Furthermore, debts and entitlements to future income streams do not seem possible to include among the givens. Disequilibrium processes that change the initial endowments and their distribution do not seem possible to include in the theory either.

3.0 Classical Political Economy

Classical political economics analyzes the conditions needed to ensure the reproduction of society. For the theory of value and distribution, the givens are:

• Technology.
• Requirements for use, which I take as net output.
• Wage or the rate of profits.

The theory of value can be combined with other elements of political economy. The classicals had various theories of wages, combined with demographics. Marx rejected Malthus and developed his theory of the reserve army of labor for similar purposes. The theory is compatible with a rejection of Say's law and enduring unemployment. Many have argued for combining this theory with a long-period interpretation of Keynes' general theory. A theory of growth and the dynamics of technical change can be built upon this theory of value and distribution.

Utility Maximization A Tautology?

Economists proved over half a century ago that certain stories are unfounded in the theory. For example, one might think that if some workers are involuntarily unemployed, a drop in real wages would lead to a tendency for the labor market to clear. The Cambridge Capital Controversy revealed some difficulties. In response, some economists turned to the Arrow-Debrue-McKenzie model of intertemporal equilibria in which it is not clear that one could even talk about such concepts. The Mantel-Sonnenschein-Debreu theorem shows that this model lacks empirical content. Utility theory provides a closure for some models. Formally, one can demonstrate the existence of equilibria under certain assumptions. But existence does not get one very far.

My purpose of this post is to note that some saw utility theory as a useless tautology at the time of the marginal revolution:

"It is interesting, in this connection, that the earliest critics saw in the theory of marginal utility what we have called a behaviourist theory of choice ... and used exactly the same arguments against it which will be used below against this latter version. Thus [John] Cairnes wrote about Jevon's theory: 'What does it really amount to? In my apprehension to this, and no more - that value depends upon utility, and that utility is whatever affects value. In other words, the name "utility" is given to the aggregate of unknown conditions which determine the phenomenon, and then the phenomenon is stated to depend upon what this name stands for.' Jevon's theory was believed to say no more than this: 'that value was determined by the conditions which determine it - an announcement, the importance of which, even though presented under the form of abstruse mathematical symbols, I must own myself unable to discern'. Some Leading Principles of Political Economy, 1874, p. 15.

[John] Ingram took the same view in A History of Political Economy, 1888, ed. by Ely, 1915, p. 228 and passim. Cairnes, Ingram, and other early critics of marginal utility had, however, directed their criticism also against the mathematical method generally, and the discussion went soon into other channels. The marginalists met the criticism by claiming to be proponents of logical and mathematical method and their tautological psychology thus escaped its well-deserved criticism." -- Gunnar Myrdal (1953) The Political Element in the Development of Economic Theory (trans. by Paul Streeten, Routledge & Kegan Paul, p. 231.

Obviously, Cairnes and Ingram could not have known about results demonstrated a century later. Utility theory manages simultaneously to not say anything about market phenomena, to not be good armchair theorizing, and to be empirically false at the level of the individual.

Jeremy Rudd: "Why I hate economics"

Jeremy Rudd addresses the Cambridge Society for Economic Pluralism

Jeremy Rudd has written:

Mainstream economics is replete with ideas that 'everyone knows' to be true, but that are actually arrant nonsense. For example, 'everyone knows' that:

• aggregate production functions (and aggregate measures of the capital stock) provide a good way to characterize the economy's supply side;
• over a sufficiently long span - specifically, one that allows necessary price adjustments to be made - the economy will return to a state of full market clearing; and
• the theory of household choice provides a solid justification for downward-sloping market demand curves.

None of these propositions has any sort of empirical foundation; moreover, each one turns out to be seriously deficient on theoretical grounds¹. Nevertheless, economists continue to rely on these and similar ideas to organize their thinking about real-world economic phenomena. No doubt one reason why this situation arises is because the economy is a complicated system that is inherently difficult to understand, so propositions like these - even though wrong - are all that saves us from intellectual nihilism. Another, more prosaic reason is Stigler's (1983, p. 541) equally nihilistic observation that 'it takes a theory to beat a theory.'

Is this state of affairs ever harmful or dangerous? One natural source of concern is if dubious but widely held ideas serve as the basis for consequential policy decisions².

¹ For a useful brief against production functions, see Felipe and Fisher (2003); for the case against capital aggregates, see Brown (1980). The idea that the inherent stability of the economy is a concomitant of general-equilibrium theory is difficult to entertain seriously after giving Fisher (1983) close study; see Grandmont (1982) for some related macroeconomic arguments. Finally, Hildenbrand (1994) provides a sobering corrective to first-year demand theory.

² I leave aside the deeper concern that the primary role of mainstream economics in our society is to provide an apologetics for a criminally oppressive, unsustainable, and unjust social order.

The above quote is from a paper about inflations expectations. I wondered how far and on what grounds Rudd thinks this arrant nonsense extends. The talk in the video linked to the top of this post helps answer this question.

What Are Prices Of Production?

Suppose one rejects the labor theory of value as a theory of prices. Or, even more, one could reject Marx's theory of value in volume 1 of Capital. Still, one could elaborate the theory of prices of production. In my published works, I have tried to extend the theory a step or two. And the theory of prices of production is opposed to a marginalist theory, a theory of supply and demand, if any such coherent theory exists.

In this post, I offer one explanation of the setting of the theory of prices of production. I am heavily indebted to Alessandro Roncaglia. Heinrich Bortis is another point of reference here. As usual, my favorite textbook expositions of the details of prices of production are by Luigi Pasinetti and Heinz Kurz and Neri Salvadori. I have yet to read Fabio Petri's recent textbook.

Suppose, for purposes of exposition, time is broken up into discrete intervals, namely, years. And the economy to be considered is a capitalist economy. Managers of firms, at the start of the year, hire so many workers and buy so many commodities on the market for fuel, raw material, tools, and so on.

One can imagine taking a snapshot at the end of the year, after the harvest. Produced commodities are in the hands of the (owners of) firms which have produced them. They need to be redistributed, among industries and among consumers, for production to continue.

Workers will purchase some commodities, with their wages and through a retail sector. Capitalists will also purchase some commodities for consumption. Firms that continue in business will buy their needed inputs from firms in other industries to continue production in the next year. Some firms will retain some of their output for use in production. I am thinking, for example, of seed in agriculture. Used machinery or a plant can be thought of as jointly produced with a more obvious commodity. Joint production proper occurs in oil refineries and breweries, I guess.

A realization problem arises here. Some will find that the (market) prices at which they buy and sell deviate from what they expected. Capitalists had certain expectations and plans when they made production decisions at the start of the year, and they may find those plans incapable of being realized at the end of the year.

But one can ask what must be prices be such that capitalists would find no need to modify their plans? These are prices of production. In a competitive capitalist economy, one assumes a common rate of profits rules in all industries. In calculating prices of (re)production, one takes either the real wage or the rate of profits as given. One might think of the wage as embodying all sorts of conventions and norms about what workers in different strata are expected to be able to purchase. At any rate, prices of production allow buying and selling that go on after the harvest to be such that produced commodities are redistributed such that a capitalist economy can be reproduced.

Some points on this abstract description of a capitalist economy:

• Decisions on what and how much to produce are made upstream from the realization problem, so to speak. At no point in time can one simultaneously validate current decisions.
• Decisions on production also generate, at the end of the year, the income used to purchase the output. Many of these decisions are for the production of capital goods quite distant from consumption.
• The workers are are hired with the promise of a payment of a money wage. The possibility arises of a conflict over distribution at the end of year in which total money claims add up to more than the output produced.
• Say's law is not assumed. Realization problems may lead to some capitalists having more unused capacity than planned or too little capacity. (Typically, firms plan to have some unused capacity so as to meet unanticipated demands.)
• No need exists to talk about supply and demand functions in explaining prices of production. No assumptions are made about any tendency for the labor market to clear in calculating prices of production.
• Perhaps capitalists can approximate prices of production, given accounting conventions about markups. Would deviations of market prices from prices of production be taken into account when they revise their plans? Or should such a story only be concerned with market prices?
• The equations for prices of production provide an open model, in some sense. The level of aggregate demand and the distribution of income are taken from outside the model.

I hope you can see some family resemblances between the approaches of Sraffa and Keynes to economics. A parallelism to the works of Marx also exists here.

Von Mises Confused About Formal Reasoning, Praxeology

1.0 Introduction

In his book, Human Action, Ludwig von Mises defines 'praxeology' as the science of human action. He says that it is a subject of formal reasoning. Human action is conscious action in which the actor attempts to decrease felt uneasiness. 'Catallactics' is a subset of praxeology treating market exchanges. But von Mises is quite confused.

2.0 Does Formal Reasoning Enlarge Our Knowledge?

Von Mises does not know. At one point, he says formal reasoning does enlarge our reasoning. And he takes geometry as an example:

"All geometrical theorems are already implied in the axioms. The concept of a rectangular triangle already implies the theorem of Pythagoras. This theorem is a tautology, its deduction results in an analytic judgment. Nonetheless nobody would contend that geometry in general and the theorem of Pythagoras in particular do not enlarge our knowledge. Cognition from purely deductive reasoning is also creative and opens for our mind access to previously barred spheres. The significant task of aprioristic reasoning is on the one hand to bring into relief all that is implied in the categories, concepts, and premises and, on the other hand, to show what they do not imply. It is its vocation to render manifest and obvious what was hidden and unknown before." -- Von Mises, Human Action, Chapter II, Section 3. The a priori and reality

Von Mises makes a distinction between class and case probability. Class probabilities can be characterized by relative frequencies. Think of craps or blackjack. Case probabilities deal with uncertainity, where events cannot be repeated in identical circumstances. A horse race starts to be uncertain. But what about the prospects of a general European war in the next twenty years? Of course, von Mises does not reference Frank Knight or John Maynard Keynes.

Class probability can be formalized by Kolmogorov's axioms. But, strangely enough, von Mises claims that formal reasoning here cannot enlarge our knowledge:

"We know, for instance, that there are ninety tickets in a lottery and that five of them will be drawn. Thus we know all about the behavior of the whole class of tickets. But with regard to the singular tickets we do not know anything but that they are elements of this class of tickets...

...For this defective knowledge the calculus of probability provides a presentation in symbols of the mathematical terminology. It neither expands nor deepens nor complements our knowledge. It translates it into mathematical language. Its calculations repeat in algebraic formulas what we knew beforehand. They do not lead to results that would tell us anything about the actual singular events. And, of course, they do not add anything to our knowledge concerning the behavior of the whole class, as this knowledge was already perfect- or was considered perfect-at the very outset of our consideration of the matter.

..It is a serious mistake to believe that the calculus of probability provides the gambler with any information which could remove or lessen the risk of gambling. It is, contrary to popular fallacies, quite useless for the gambler, as is any other mode of logical or mathematical reasoning." -- Von Mises, Human Action, Chapter VI, Section 3. Class probability

I guess von Mises did not get his brother Richard, the more intelligent one, to review his work. I gather that von Mises was not exposed to David Hilbert's notion that axiomatic reasoning in mathematics is not about physical things in the external world, albeit he does have an observation about Einstein that suggests maybe he was.

2.0 Can Logic Describe Events In Time?

In discussing this question, von Mises makes an elementary mistake in reasoning:

"Logic and mathematics deal with an ideal system of thought. The and implications of their system are coexistent and interdependent. We may say as well that they are synchronous or that they are out of time. A perfect mind could grasp them all in one thought. Man's inability to accomplish this makes thinking itself an action, proceeding step by step from the less satisfactory state of insufficient cognition to the more satisfactory state of better insight. But the temporal order in which knowledge is acquired must not be confused with the logical simultaneity of all parts of this aprioristic deductive system. Within this system the notions of anteriority and consequence are metaphorical only. They do not refer to the system, but to our action in grasping it. The system itself implies neither the category of time nor that of causality. There is functional correspondence between elements, but there is neither cause nor effect.

What distinguishes the praxeological system from the logical system epistemologically is precisely that it implies the categories both of time and of causality. The praxeological system too is aprioristic and deductive. As a system it is out of time. But change is one of its elements. The notions of sooner and later and of cause and effect are among its constituents. Anteriority and consequence are essential concepts of praxeological reasoning. So is the irreversibility of events. In the frame of the praxeological system any reference to functionaI correspondence is no less metaphorical and misleading than is the reference to anteriority and consequence in the frame of the logical system." -- Von Mises, Human Action, Chapter V., Section 1. The temporal character of praxeology

I more or less agree with von Mises that an axiomatic system does not exist in time, despite the fact that mortals, in stepping through deductions in such a system, use up time. But these claims' are distinct from the idea that such a system cannot characterize events in time in some sense. In fact, temporal logic exists. I suppose I could stand to know more about C. A. R. Hoare's Communicating Sequential Processes (CSP). In one of my papers, I illustrated a trace of an algorithm.

3.0 Is Logic Built Into The Human Mind?

I think the answer to this question to be negative. I think I am agreeing with dominant trends in logic and philosophy for a century and a half. Von Mises, though, answers this question in the positive:

"The human mind is not a tabula rasa on which the external events write their own history. It is equipped with a set of tools for grasping reality... the logical structure of human reason.

praxeology ... is human because it claims for its theorems, within the sphere precisely defined in the underlying assumptions, universal validity for all human action

the logical structure of mind is uniform with all men of all races, ages, and countries -- Von Mises, Human Action, Chapter II, Section 2. The formal and aprioristic character of praxeology.

Is this logic build into all minds propositial logic? Predicate logic? Modal logic? Three-valued logic? Von Mises does not say. He does say that praxeology need not take into account the findings of psychology.

4.0 What Does von Mises Mean by a 'Theorem'?

Maybe the issue is with von Mises' understanding of logic and formal reasoning. He dismisses the call for axioms and says his 'theorems' are drawing out the concepts implicit in the categories of human action. To me, this suggests an approach drawing on Immanuel Kant. Of course, von Mises does not reference Kant.

Anyways, let us look at some examples of what von Mises says are theorems:

"Thinking is to deliberate beforehand over future action and to reflect afterward upon past action. Thinking and acting are inseparable. Every action is always based on a definite idea about causal relations. He who thinks a causal relation thinks a theorem. Action without thinking, practice without theory are unimaginable. The reasoning may be faulty and the theory incorrect; but thinking and theorizing are not lacking in any action. On the other hand thinking is always thinking of a potential action. Even he who thinks of a pure theory assumes that the theory is correct, i.e., that action complying with its content would resuit in an effect to be expected from its teachings. It is of no relevance for logic whether such action is feasible or not." -- Von Mises, Human Action, Chapter IX, Section 1. Human Reason

The above sounds implausible to me. Not everybody acting, including me, can always articulate a proposition about why they are doing what they are doing. I suppose one could read von Mises as narrowing the concept of human action, contrary to his intent.

Here is another example:

"In the concept of money all the theorems of monetary theory are already implied. The quantity theory docs not add to our knowledge anything which is not virtually contained in the concept of money. It transforms, develops, and unfolds; it only analyzes and is therefore tautological like the theorem of Pythagoras in relation to the con- cept of the rectangular triangle." -- Von Mises, Human Action, Chapter II, Section 3. The a priori and reality

To my mind the properties of money, as a means of exchange, a unit of account, and a store of value, do not seem to be of the nature to easily support formal reasoning. Various assets have some degree of moneyness in various communities.

Von Mises nowhere lays out the basis of his formal reasoning in one compact place. He makes up his principles as he goes. For example, consider the tradeoff between labor and leisure. Here is some sentences about his assumptions:

"The disutility of labor is not of a categorial and aprioristic character. We can without contradiction think of a world in which labor does not cause uneasiness, and we can depict the state of affairs prevailing in such a world. But the real world is conditioned by the disutility of labor. Only theorems based on the assumption that labor is a source of uneasiness are applicable for the comprehension of what is going on in this world." -- Von Mises, Human Action, Chapter II, Section 10. The Procedure of Economics

And when it comes to intertemporal tradeoffs, he invents another principle.

"The theorem of time preference must be demonstrated in a double way. First for the case of plain saving in which people must choose between the immediate consumption of a quantity of goods and the later consumption of the same quantity. Second for the case of capitalist saving in which the choice is to be made between the immediate consumption of a quantity of goods and the later consumption either of a greater quantity or of goods which are fit to provide a satisfaction which-except for the difference in time-is valued more highly. The proof has been given for both cases. No other case is thinkable." -- Von Mises, Human Action, Chapter XVIII, Section 2. Time Preference as an Essential Requisite of Action

Von Mises just does not seem to appreciate the requirements for formal reasoning. Here is how some recent authors start to explain the difference between formal and informal reasoning:

Here are two tasks for you to try:

1. Define "chair". That is, give a set of properties so that:
1. everything which is a chair has those properties;
2. everything which has those properties is a chair;
3. everything you might deduce from that set of properties holds for all chairs.
2. Without giving the formal definition, describe the notion of a basis of a vector space.

Task 1 is hard, if not impossible. Dictionaries give definitions of concepts such as chair, but these are concise descriptions designed to capture pre-existing concepts; they do not, and are not designed to, satisfy constraints (a), (b) and (c). Indeed, most of us have probably never looked at a dic- tionary definition of "chair", but our experience with chairs means that we have no problem recognising and using them in everyday life (Vinner, 1976; Vinner, 1991; Edwards & Ward, 2004)

Task 2, on the other hand, is relatively easy. It may be somewhat unsatisfying to give an informal description of a concept such as basis, because we know that in doing so we are glossing over technical subtleties. But most of us do such things regularly in our teaching and in talking to colleagues. When introducing the concept in a lecture, we probably provide a formal definition and also try to give students a sense of the concept by saying something like "as small a set of vectors as possible, from which you can make all the others in the space". Indeed, we move easily between informal statements that describe a concept and a formal definition that, unlike a dictionary definition, prescribes what is (and is not) an instance of that concept. We recognise, however, that there is a huge functional difference between the two types of statement, and that formal definitions serve to structure the world of mathematics precisely because they do satisfy constraints (a), (b) and (c). -- Lara Alcock and Adrian Simpson, Ideas from Mathematics Education

Spinoza's Ethics offers a system laid out with formal reasoning, yet treating a subject that many today think resistant to such a treatment. Von Mises talks a good game, but does not do this.

5.0 Conclusion

I have hardly exhausted all the problems in von Mises' unscholarly book. It is fine for a researcher to produce a work against the dominant trends of a discipline. Israel Kirzner can argue that there are some insights here missed by, for example, Lionel Robbins's definition of economics. I, however, find the confusion to outweigh any insight.

Reference

• Ludwig von Mises. 1966. Human Action Third revised edition. Chicago: Contemporary Books.

Direct And Indirect Methods, Axioms And Algorithms For The Choice Of The Technique

1.0 Introduction

Kurz and Salvadori (1995) explain prices of production with two methods of analysis: the direct method and the indirect method. The indirect method, for the circular capital case, involves the creation of the wage frontier, the most well-known diagram to come out of Sraffa (1960). The direct method characterizes a system of prices of production by axioms, while the indirect method suggests algorithms for finding cost-minimizing techniques.

2.0 The Direct Method

In both methods, the given technology is characterized as a set of processes. A process is specified as the quantities of inputs and the quantities of outputs for a given level of operation. In the case of reproducible natural resources, that is, land, the quantity available of each quality of land should be specified. I do not think that non-reproducible natural resources fit comfortably in this model; some work has been done on the corn-guano model exploring this.

I find it useful to assume constant returns to scale. I understand why Sraffa does not need this assumption in the first two sections of his book. He does not consider the choice of technique there or how a state can be reached in which the same rate of profits is obtained for each operated process. He considers which process is operated and the level of operation of each process as given. Sraffa explicitly says that his assumption, that no question of the returns to scale arises, does not apply to the last section, analyzing the choice of technique. I find it difficult to understand how the theory of joint production can be set out without considering the choice of technique.

Informally, the following six axioms characterize quantities and prices for a capitalist economy undergoing smooth reproduction:

1. The levels of operation of the processes comprising the technology are such that, after replacing commodities used up in production and those needed for accumulation at the given rate of growth, requirements for use can be satisfied by net output.
2. The levels of operation of the processes comprising the technology are such that one unit of labor is employed throughout the economy.
3. No pure economic profits can be made by operating any process. That is, for each process, the revenues obtained from operating it do not exceed its costs, including charges for the rate of profits, rent, and wages.
4. The price of the numeraire is unity.
5. The rule of free goods: The price of a good in excess supply (that is, with a level of production strictly exceeding its requirements for use) is zero.
6. The rule of non-operated processes: If the costs of operating a process, including charges for the rate of profits, strictly exceeds the revenues obtained from that process, it is not operated.

Kurz and Salvadori set out these axioms for specific models, along with non-negativity conditions. In models of rent, one discards the second axiom; scale matters. The most general model, I guess, is that of full joint production. What can be deduced from the axioms varies among these models.

3.0 The Indirect Method

One can set out the indirect method by applying combinatorics, in which one looks at all possible techniques that can be constructed from the processes comprising the technology. Discard those techniques that cannot satisfy requirements for use. In the circulating capital case, each technique yields a system of equations with one degree of freedom. These equations can be solved. So each technique has a wage curve, in which the wage is lower, the higher the rate of profits. All these curves can be graphed on the same graph, and the outer wage frontier shows which technique is cost-minimizing at any given wage or rate of profits.

How can a combinatorial explosion be avoided in this analysis? By applying certain algorithms which do not require one to consider every technique. Christian Bidard champions the Lemke algorithm for the case of fixed capital. As in the case of the simplex method for linear programs, one does not need to consider every feasible technique in finding the cost-minimizing technique for a given wage or rate of profits.

4.0 Questions

Different, but related questions, arise for the two methods. For the direct method, one asks, what conditions must technology satisfy such that a solution of quantities and prices exist? When is this solution unique? For the case of circulating capital, one looks at the Hawkins-Simon condition, the Perron-Frobenius theorem, and the misleadingly-named non-substitution theorem. In the case of general joint production, the special case in which the rate of profits is equal to the rate of growth is of interest. I suppose research questions might still revolve about how many of the nice properties of circulating capital carry over to models that are intermediate between this case and full joint production. For example, has any work been done on combining a fixed capital model with a model of extensive rent? Biao Huang recently found that revisiting the fixed capital model was worthy of research. Relaxing the assumption of free disposal is important for investigating environmental concerns.

For the indirect method, I ask on what platforms are these algorithms executing? When I apply numerical methods for finding fluke switch points, I am definitely not making any claims about how markets work. I think my application of linear programming and duality theory in my 2005 Manchester School article is another case of an external analyst examining an economic model. But sometimes, as in my 2017 ROPE article, an algorithm is described that can be executed by an abstract market. At least this seems to be Bidard's view. And these algorithms might even be able to be executed in parallel by, say, accountants working for different firms in different industries. What I would like to see, however, is how market structures, how bids and asks are resolved, for example, enters into these algorithms. Be that as it may, one can ask which algorithms converge. How fast? Is the point to which they converge unique and independent of the initial condition?

References

• Christian Bidard. 2004. Prices, Reproduction, Scarcity. Cambridge University Press.
• Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis. Cambridge University Press.
• Keiran Sharpe. 1999. Note and comment: on Sraffa's price system. Cambridge Journal of Economics 23(1): 93-101.
• Piero Sraffa. 1960. The Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory. Cambridge University Press.
• K. Vela Velupillai. 2021. Definitions, assumptions, propositions and proofs in Sraffa's PCMC. In A Reflection on Sraffa's Revolution in Economic Theory (ed. by Ajit Sinha). Palgrave
• Ludwig Wittgenstein. Remarks on the Foundations of Mathematics, revised edition.
• J. E. Woods. 1990. The Production of Commodities: An Introduction to Sraffa. Macmillan.

External Influences On Academic Economics?

1.0 Introduction

A question has arisen elsewhere. Why, except for an interlude during the post war golden age, has a nineteenth century orthodoxy dominated economics departments and treasury departments around the world? Here I do not investigate the details of this orthodoxy or if it does dominate.

2.0 An Authoritarian Point of View

Some people believe that some are better than others. They want to live in a world where those at the top tell those below what to do, and those below jump.

One might think that it would be hard to find people willing to explicitly articulate these feelings in public. But you can find, if you look, Republican candidates for elected offices saying it was a mistake to allow woment to vote or that interracial marriage should be outlawed.

Some who support plutocracy, maybe unknowingly, would rather claim they are for meritocracy. The extreme distribution of wealth and income in, say, the United States is a difficulty for this view. The rewriting of laws over decades to (p)redistribute income upwards is another inconvenience for this point of view. Advocates for such may be in the grip of a reification in which they naturalize political choices. If a meritocracy was ever momentary established, those at the top could still be expected to try to structure society for their advantage and to attempt to get the best for their spawn.

The reproduction of society is a focus of my favorite schools of economics. Persistent high unemployment and a weak social safety net are useful for sustaining plutocracy. Those at the top want those at the bottom worried about how to feed themselves, not in whether they can participate in governing themselves. Those in middling positions should be economically anxious and worry about falling down. A lack of solidarity between those at your level or with those below is useful for plutocrats. Divisions between workers of various sorts, between races, between men and women, between sexual majorities and minorities are all to be encouraged.

3.0 A Humane Point of View

Human beings do not exist for the economy, but the economy, if it exists, exists for human beings. One assesses how well an economy works by how well it elevates those at the bottom. Are they able to feed, clothe, and shelter themselves? Do they have some share in the necessaries and conveniences of life? Do they participate in improvements brought about by innovations and increases in productivity? Are those at the margins increasingly brought into society?

Before and during the industrial revolution, people needed to work to produce the commodities needed to sustain the population. "For even when we were with you, this we commanded you, that if any would not work, neither should he eat" (2 Thessalonians 10).

This attitude is outdated when productivity is raised so high that, with appropriate distribution, all can have enough. Nor is there are virtue in producing what can be sold on the market. Somewhere, Joan Robinson said something like that the distinction between what can be marketed and what cannot is a technical accident. The expansion of national income provides employment, and, under the current system, employment is a source of income and self-esteem.

Doubtless, in a country with an Universal Basic Income, some would devote to themselves to dissipated living. From the standpoint of political economy, I do not have a problem with this.

But if the economy was structured to serve humanity, many would not feel obligated to spend all their days grubbing for a living. One might have more voluntary neighborhood associations beautifying their area. More young people might organize sports leagues and be playing pickup games. Many would spend more time in community theater or music events. Much more could be done by community groups, charities, and other voluntary civic groups. (In my personal life, I am more a patron or donor for such organizations, mostly not local, than a participant.)

The development of point of views consistent with these ideas and their implementation is and should be a threat to plutocracy.

4.0 Some Speculation

If one looks at the funding of academic economic departments, one can certainly identify promotors of authoritarianism and plutocracy.

On Equilibrium

I have found a common misrepresentation from many, including mainstream economists, is that critics of their models do not understand them or the role of the assumptions. Those mainstream economists rely on an incoherent essay from Milton Friedman to dismiss criticism of the realism of assumptions.

My favorite criticism, though, is that their conclusions do not follow from their assumptions. I like to show this by constructing numerical examples that contradict their teaching.

On the other hand, some do criticize the realism of assumptions. I have seen some complain that the economy is never in equilibrium. It is unrealistic to assume equilibrium. I often find this unconvincing.

One can go back at least as far as Adam Smith, the distinction he draws between market prices and 'natural' prices, and his metaphor of a gravitational process. At any given time, some commodities may remain unsold on the market, and the quantity demanded for some may exceed the quantity supplied at a moment in time. The rate of profits may vary among firms and industries more than one might expect because of differences in risk, the desirability of certain industries, and so on. A leveling process that may never be completed exists at a given moment in time. Capitalists, reacting to price signals, will be disinvesting in some industries and expanding in other industries.

One who studies 'natural' prices, that is, the system of prices of production, is investigating tendencies, not making a claim that equilibrium exists. Even after the marginalists started constructing an incorrect theory, they kept this approach. Alfred Marshall wrote about, market prices, the short run, and the long run. Here is Walras:

Finally, in order to come still more closely to reality, we must drop the hypothesis of an annual market period and adopt in its place the hypothesis of a continuous market. Thus, we pass from the static to the dynamic state. For this purpose, we shall now suppose that the annual production and consumption, which we had hitherto represented as a constant magnitude for every moment of the year under consideration, change from instant to instant along with the basic data of the problem... Every hour, nay, every minute, portions of these different classes of circulating capital are disappearing and reappearing. Personal capital, capital goods proper and money also disappear and reappear, in a similar manner, but much more slowly. Only landed capital escapes this process of renewal. Such is the continuous market, which is perpetuating tending towards equilibrium without ever actually attaining it, because the market has no other way of approaching equilibrium except by groping, and, before the goal is reached, it has to renew its efforts and start over again, all the basic data of the problem, e.g. the initial quantities possessed, the utilities of goods and services, the technical coefficients, the excess of income over consumption, the working capital requirements, etc., having changed in the meantime. Viewed in this way, the market is like a lake agitated by the wind, where the water is incessantly seeking its level without ever reaching it. But whereas there are days when the surface of a lake is almost smooth, there never is a day when the effective demand for products and services equals their effective supply and when the selling price of products equals the cost of the productive services used in making them. The diversion of productive services from enterprises that are losing money to profitable enterprises takes place in various ways, the most important being through credit operations, but at best these ways are slow. It can happen and frequently does happen in the real world, that under some circumstantces a selling price will remain for long periods of time above the cost of production and continue to rise in spite of increases in output, while under other circumstances, a fall in price, following upon this rise, will suddenly bring the selling price below cost of production and force entrepreneurs to reverse their production policies. For, just as a lake is, at times, stirred to its very depths by a storm, so also the market is sometimes thrown into violent confusion by crises, which are sudden and general disturbances of equilibrium. The more we know of the ideal conditions of equilibrium, the better we shall be able to control or prevent these crises." -- Walras (1954: Lesson 35, Section 322).

So Walras did not think any economy would ever be in equilibrium. On the other hand, many may incorrectly think Austrians, like Ludwig von Mises, dispensed with the assumption of equilibrium. But here he is asserting that the assumption of equilibrium is necessary for economic theory:

One must not commit the error of believing that the static method can be used only to explain the stationary state of an economy, which, by the way does not and never can exist in real life, and that the moving and changing economy can be dealt with only in terms of a dynamic theory. The static method is a method which is aimed at studying changes; it is designed to investigate the consequences of a change in one datum in an otherwise unchanged system. This is a procedure which we cannot dispense with." -- Ludwig von Mises, 1933. Intervention. (quoted by Kurz and Salvadori)

I do think, however, one can criticize the Arrow-Debreu model as not being consistent with this approach and always assuming that equilibrium exists. Any time to reach equilibrium in the Arrow-Debreu is too long. Any such equilbirum that might have a tendency to be approached cannot be expected to be consistent with the data. Many supposed dynamic models in economics are still subject to this old objection.

Many questions remain about how to analyze whatever tendencies to equilbrium that may exist. I have barely even touched on the distinction between logical and historical time, a distinction commmon to Joan Robinson and Ludwig Lachmann.

Nonsense Taught At MIT

First Lecture For MIT Microeconomics

I associate Jonathan Gruber with Obamacare. I think the Affordable Care Act is totally insufficient and a great advance. If politicians hire you to model the effects of some policy change, might you want to use, more or less, the most widely accepted techniques? I am also appreciative that I can watch this.

When you are teaching, should you present claims in the most romantic way possible?

"That is why I can teach you the entire field of microeconomics, which is really sort of - macro is kind of a fun application - micro is really economics." (around 9:20)

Thinking of (micro)economics as a matter of constrained optimization is only one approach. I like the idea of investigating the conditions needed for a capitalist economy to reproduce itself. This is mesoeconomics, I guess, but should be mentioned in an honest class on microecnomics.

From Thomas Kuhn, I know history of a subject is often widely distorted in introductory courses. Is this justification for spouting nonsense?

Adam Smith did not have a supply and demand model, that is, of an equilibrium price formed by the intersection of a supply curve and a demand curve (balderdash after about 11:23). Mashall's scissors certainly do not appear in Adam Smith's Wealth of Nations. Maybe Gruber should note the difference between market prices and natural prices. The model Gruber's teaches is known to be incoherent nonsense, not derivable from basic first principles.

Can one coherently talk about a value-free postive economics? I guess saying that a distinction exists between positive and normative economics does not say that positive economics is value-free. But it certainly suggests that. What Gruber presents (after 34:30) for examples is enlightening, albeit not necessarily in the way that he intends. Do some teachers of introductory courses talk about Schumpeter's "vision"?

If economics is a science, why do this preaching after 26:30? By the way, do the Seninelese have a capitalist economy? Or do they practice Stalinist central planning? How about the society envisioned by the P.O.U.M. in Barcelona during the Spanish Civil War?

Update (13 August 2022): Lecture 5 is on production theory, supposedly. If economists were scientist, one would not be able to discomfort them by asking about units of measure for variables in their equations, such as K.

Correspondence Between Rudiger Soltwedel And Piero Sraffa

This is C/294 in the Sraffa archives. Rudiger Soltwedel had his own letterhead.

D 66 Saarbrucken 3, 28. Febr. 1968
Waldhausweg 7
Evangelisches Studentenheim

Professor Piero Sraffa
Trinity College
Cambridge

Dear Sir,

I am student of economics at the University of Saarbrucken and I just began my finals work for my diploma.

The topic of this study that Prof. E. Schmen formulated is your essay and its title is exactly that of your book: ‘Sraffa’s production of commodities by means of commodities’.

My task is to state the intention of your book and to explain its relation to input-output analysis.

After looking around in literature I only found three reviews (AER: Reder; Ec. Journ.: Harrod; Jorn. Of Pol. Econ.: Quandt; all 1961) but nothing beyond that.

I would be very indebted to you if you could give me some hints of literature directly concerned with your book or with its subject.

At the moment, I think the aim of your study not to be a theory of distribution or a development of input-output analysis, but rather a theory of price-determination in input-output models, given the physical amount of the surplus, economy in equilibrium and infinite elasticity of factor supply. The outcome is an antithesis to what Dorfman/Samuelson/Solow said about relative prices in the Leontief-model: "... in a Leontief-technology relative prices can’t change". (Lin. Programming …, p. 224) in saying that they have to change with changes in distribution of the surplus, And, finally, the profitability of distinct methods of production is dependent on the distribution of the surplus to wages or profits respectively.

This is a bird-eye look on your essay and it is not equivalent to a complete understanding of it. In particular it is the chapter V that charges my brains with its argumentation of extreme density.

I hope that you are willing to excuse my attack on the ‘pater spiritorum’ and would be very thankful for some advice on your part.

Yours respectfully,
Rudiger Soltwedel

Underlines are presumably Sraffa's. "in equilibrium" and "elasticity of factor supply" have underlines in squiggly lines, while the others are solid lines.

Trinity College
Cambridge
1.3.68

Dear Mr. Soltwedel,

Thank you for your letter. I shall try to help you as far as I can in a short letter. As regard my aims, I have kept them in the background in the hope that the constructions offered might be of use to others, who have different standpoints. I have given hints in the Preface and in Appendix IV. The reviews you have are not very helpful. Reder, in particular, is a string of misunderstandings. A good review is that of Peter Newman, in Schweitrerische Zeitschrift fur Volkswirtschaft u. Statistik, No. 1 of 1962, p. 58-75. I disagree with many of his points & had some correspondence with him; we came only to partial agreement, but his review is a good piece of work. There were also good reviews in the Economic Record (Australia, Sept. 1964, p. 442 ff. by Harcourt and Massaro) and in the Economic Weekly (Indian, 24 Aug. 1963, by Krishna R. Bharadwaj). By the way, I replied to Harrod in the June 1962 number of the Economic Journal (p. 477-9).

As regard your own your own interpretation, I must say frankly that you have gone astray the moment you speak of "equilibrium" or of "elasticity of factor supply": all the quantities considered are what can be observed by taking a photograph. There are no rates of change, etc. This point of view was that of the classical economists (e.g. Ricardo) whereas supply & demand curves were introduced in the middle of the 19th century. Economists are now obsessed with them and cannot think without them. My chapter V, which gives you such a headache, could be understood as an attempt to solve a problem set out by Ricardo, & which I described in my Introduction (sections IV & V) of Vol. I of the Works of Ricardo, 1951.

With good wishes for your work,

Yours sincerely
Piero Sraffa

Any errors in journal names, numbers, pages are presumably from my transcription.

66 Saarbrucken 3, 12. ??. 1968
Waldhausweg 7
Evangelisches Studentenheim

Dear Sir,

I thank you very much for your kind reply to my letter.

There was good progress in my work based on your remarks and on the reviews mentioned, in particular the mathematical proof of some propositions in the work of Newman was of great help.

But there is a point in nearly all reviews I don’t agree with and that receives illumination by your book: the claim of the rates of profits being the same in all industries is interpreted as a condition of long run competitive equilibrium prices. Now the structure of your economy is far away from ??determined by competition that this approach does not fit the problem. It looks like a challenge consequent upon a distinct notion of justice in distribution (that could, however, be attained through perfect competition). Unfortunately, your book provides no explanation.

I hope it not to be too unconscionable asking for another explanation.

Yours sincerely,
Rudiger Soltwedel

Sraffa has handwritten “given up” on the top of this letter.

On Sraffian Methodology

I do not know if I will keep on, but I thought I might present a series of posts expanding on this one. By the way, I should have said there that the maximum rate of profits is the reciprocal of the organic composition of capital in Sraffa's standard system, not the actual system.

Sraffa's model is descriptive, based on objective data that can be observed for one production period. This data, at least through the first three chapters of The Production of Commodities by Means of Commodities, consists of:

• The gross quantities produced over the production period, in physical units.
• The proportion of labor employed in each industry.
• The commodities that are used as inputs in each industry.
• The wage, expressed as a proportion of the value of the net output produced in the period.

Assume that the same rate of profits is made in each industry. Evidently, this model is of a more or less competitive capitalist economy. Then, assuming a viable economy, prices of production are determined by the data.

Sraffa extends this approach to consider joint production, including fixed capital and rent. He often does not explicitly state assumptions or, if so, not in any detail. Furthermore, how this approach fits with a more thorough analysis of capitalist economies, at least, has been a subject of debate ever since the publication of his book.

New York City Subway: A Parable

A number of years ago, I was in the subway station under Times Square in New York City. I must have looked lost, because this fellow came up to me and asked me where I was going.

I said, "A bookstore, The Strand. I like to see what they have in their economics section. I am trying to decide if I should take the cross-town shuttle and go south from Grand Central."

He said, "I am an economist myself. You can have this subway map." And he handed me a map of the tube in London.

"This map is inaccurate."

"Of course. A map on a one-to-one scale would not be useful."

"I don't mean that. Here in New York, there is no circle line."

"It's called 'abstraction'. We don't care about curves between stations that do not matter."

"But this is just wrong for here."

"All models are wrong. Some are useful."

I finally saw I should just thank him, take the map, and back away. As I did, I heard him mutter to himself, "That guy does not understand scientific methodology."

I trust mainstream economists to help gather data for, for example, Simon Kuznets' National Income and Product Accounts and, for some, to provide guidance among data sources.

On My Research Program

"I know not how I may seem to the world, but as to myself I seem to have been only like a boy playing on the sea-shore and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me." -- Isaac Newton (apocryphal?)

For the past couple of years, I have been pursuing a research program that I seem to have stumbled upon. I am looking for fluke switch points, where these fluke switch points partition certain parameter spaces. The analysis of the choice of technique is supposed to be qualitatively invariant, in some sense, in each region formed by these partitions, but varies among regions.

I have tried to define a taxonomy for such fluke switch points. Using an example, I have explored structural dynamics. Analyzing fluke switch points in models of fixed capital lets me see maybe more deeply into the incoherence of Austrian and marginalist approaches. Lately, I have been considering a parameter space of relative markups. Even more recently, I have been considering models of extensive rent.

Mathematically, these post-Sraffian models I have been exploring are open. Given parameters characterizing the technology and relative markups among industries, the distribution of income can vary with one degree of freedom. But if the wage, for example, and the size and composition of the net product is given, the rate of profits and the price of each commodity is determined. This is a matter of mathematics, close to accounting. Is my approach compatible with Ajit Sinha's reading of Sraffa's work as an approach akin to geometrical reasoning?

I do not know that Tony Lawson would accept that these models are ontologically open in his sense. Similarly, Nicholas Georgescu-Roegen made a distinction between what he called arithmorphic and dialetic reasoning. In my approach, I emphasize how quantitative perturbations of parameters leads to qualitative change in admittedly static models. I limit myself to discovering structures at the level of mesoeconomics, not visible at the level of individual transactions or an individual (non-vertically integrated) industry.

I rarely comment on whether or not I am taking an empirical economy as given. My approach certainly relates to Leontief input-output matrices, which can be constructed or approximated from National Income and Product Accounts (NIPAs). The econometrician would probably also want prices indices for individual industries. At a given point of time, one might say a process is dominant in each industry. But some firms might be still operating old processes, and others might be introducing new processes with which they hope to make super normal profits for a time. This observation provides some justification for considering the choice of technique. I often postulate continuous declines in coefficients of production, following Pasinetti's lead, or variations in relative markups. Is this a matter of counter-factual reasoning that Sraffa would reject?

I am aware that my models are not set in historical time. This is a point of contention for some Post Keynesian, such as Lars Syll. Do at least some of my partitions have implications for the dynamics of how or whether market prices approach prices of production? This is a question that I will continue not to address. I found intriguing this talk by Ian Wright, with accompanying handout.

Research in flukes may lead to more acceptance of possibility of reswitching, capital reversing, reverse substitution of labor, recurrence of processes. I wonder if somebody that understands something about algebraic geometry could summarize my approach more shortly, but even more abstractly. I hope and wish that I can read sometime somebody extending this research. Some sort of structures definitely seem to exist in these parameter spaces.

The LTV And Commodity Fetishism

You will occasionally come upon supposed refutations of Marx's theory of value that I find just ignorant. One might talk about two divers. One comes up with a handful of sand, and the other comes up with a pearl. They have put in the same labor, but their products are of quite different exchange values. Or consider the labor that goes into making a useless product, something that cannot be sold as a commodity on a market. Obviously, labor does not create value.

A refutation can only be effective, at least among serious people, if it attempts to start with an understanding of the idea being attacked. A critique could be immanent and transcend the position it starts with. Or it can end up just rejecting that position.

I am not sure why I included a bit about commodity fetishism in my Frequently Asked Questions about the Labor Theory of Value. Apparently, one of my most popular posts is this one, in which I collect passages in Marx on vulgar political economy, commodity fetishism, and the illusions created by competition.

Marx, in Capital, for example, is analyzing the conditions that allow for a capitalist society to continue, to be self reproducing, albeit with fits and starts. One condition is that labor be distributed among many different concrete activities. For car and trucks to be produced, workers, besides making cars, maybe must be making tires out of rubber and steel out of iron, for example. And trucks or locomotives might be being driven to deliver steel or tires to outside of Detroit. The workers performing these activities are in a social relationship, but they do not see this. Even the managers of firms do not see this. Rather, this social relationship between workers is brought about by selling and buying commodities, such as tires, steel, and cars. Prices bopping about on markets bring about and maintain the relationships between workers. One can see why an analysis of capitalism might begin with an analysis of a commodity.

Individuals living in a self-reproducing society take on various roles, roles that cannot be defined in terms of a single individual or single transaction. Teachers cannot exist without students sometimes listening. And for a teacher to be a teacher, there cannot be just one teacher who once taught one student for one session. Instead, to be a teacher requires that one sometime has taught a student week after week. Nor can a king exist, Antoine de Saint-Exupery to the contrary, alone on an isolated asteroid. Subjects also must exist who acknowledge at least the possibility of sovereignty.

Marx treats the capitalist as 'capital personified'. The capitalist repeatedly uses money to buy raw materials and machinery (means of production) and hire workers (labor power). The workers make a commodity under the direction of the capitalist, and the capitalist owns what the worker makes. The capitalist must then sell the produced commodities on the market. The repeating of this process, time after time, is what makes a capitalist a capitalist according to Marx.

Neither capitalists nor workers calculate labor values. When the capitalist sells commodities on the market, he does not view the commodity as a 'material receptacle of homogeneous human labour'. And capitalists are not required to recognize that the relative prices of commodities express a social relationship characterizing how the total workforce is distributed among their establishments in the various industries in which production goes on in parallel.

Workers pressing for higher wages, less hours, and better working conditions also need no awareness of the labor time embodied in the commodities that they produce and in the commodities embodied in their wage. I take no issue, though, that it is helpful for workers and their advocates to have some awareness of the 'laws of motion' of the mode of production for the society in which they live.

It is a necessary consequence of this analysis that sometimes capitalists will direct workers to make something that cannot be sold as a commodity on the market. In some industries and processes, one expects a certain average failure rate. In oil drilling, for instance, one would expect a certain number of wells to fail. This rate may be lowered by technological advances, such as in controlled denotations and in signal processing applied to returns from various kinds of sensors. Likewise, if all of a company's research and development efforts pay off, it is not doing R and D right.

The deviation of market prices from prices of production is another reason sometimes some commodities cannot be sold on the market for prices that cover the average rate of profits. It is precisely the capitalists reactions to these deviations that bring about the social relationship between workers.

In this post, I have not even defined labor values, much less made any claims about quantitative relations between prices and labor values. I have also deliberately not used the phrase 'socially necessary abstract labor time' (SNALT). I think it clear that Marx thought that none of his claims depended on prices of production being proportional to labor values. I end where one could start with a mathematical treatment of Marx's theory of value. Only then could one argue about whether Sraffa's standard commodity does or does not provide a solution to the transformation problem.

References

• Arato, Andrew and Paul Breines. 1979. The Young Lukács and the Origins of Western Marxism. The Seabury Press.
• López, Daniel Andrés. 2019. Lukács: Praxis and the Absolute. Brill Books.
• Lukács, Georg. 1967. History and Class Consciousness. Trans. by Rodney Livingston.. Merlin.
• Rubin, Isaak I. Essays on Marx's Theory of Value.

Nicholas Georgescu-Roegen On Mathematical Methods In Economic Science

I have long been convinced that many mainstream economists, however they performed under hazing, do not understand mathematics.

"T. C. Koopmans, perhaps the greatest defender of the use of the mathematical tool in economics, countered the criticism of the exaggeration of mathematical symbolism by claiming that the critics have not come forward with specific complaints. The occasion was a symposium held in 1954 around a protest by David Novick. But, by an irony of fate, some twenty years later one of the most incriminating corpora delicti of empty mathematization got into print with the direct help of none other than Koopmans. R. J. Aumann had already published in Econometrica an article dealing with the problem of a market in which there are as many traders as the real numbers, that is, as many as all the points on a continuous line. In 1972, Koopmans presented to the National Academy of Sciences a paper by Donald Brown and Abraham Robinson for publication in its official periodical. The authors assumed that there are more traders even than the elements of the continuum. Now, since the authors of both these papers and Koopmans are well versed in mathematics, they must have known the result proved long ago by George Cantor, namely, that even an infinite space can accomodate at most a denumerable infinity of three-dimensional objects (as the traders must necessarily be)." -- Nicholas Georgescu-Roegen (1979) Methods in Economic Science. Journal of Economic Issues, XIII (2): 317-328.

I do not intend to get a Twitter account. Yesterday(?) some economist illustrated what they learn by tweeting a screenshot of a couple of pages from Mas-Colell, Whinston, and Green..

Why Do Mainstream Economists Not Make More Out Of The CCC?

Marx is mostly right.

That is the conclusion one should draw from capital theory. But honestly understanding how we are fed, clothed, and housed under capitalism is not what academic economics is about.

Ownership of property in, say, the United States results in the generation of income. This income takes the form of interest on debt, dividends, capital gains, rent, and so on. Many of those who are among the most wealthy often have returns to property ownership as their only source of income.

Overall, laborers work within a given environment to recreate the capital goods used up in production and to produce more. The source of the returns to property ownership comes from paying workers less than what they produce, over and above the constantly reproduced capital. The owners of capital direct and control the workers and the environment in which they work, in hierarchical structures, so as to attempt to ensure the surplus is as large as possible.

Marx provides a vocabulary to talk about the above qualitative outline, to understand the formal and real subsumption of labor.

Marx provides many details to investigate and modify. I do not think the law of the tendency of the rate of profits to fall (TRPF) can be deduced from the remainder of his system. But just like a simple labor theory of value, it seems to work surprisingly well empirically. When one tries to make sense about the stagflation of the 1970s and the transition from the post war golden age to the neoliberal era, trends in the rate of profits seem quite important.

How important is the question of labor values versus prices of production in any quantitative analysis built on this basis? One can say a lot while confining one's attention to employment multipliers and prices of production. The non-applicability and incoherence of the theory of supply and demand is a major point of the Cambridge Capital Controversy. Supply and demand functions no longer should appear in any long run theory, in any investigation of persistent trends in capitalist economies.

And, of course, Leontief figured out how to organize data for empirical and quantitative investigations along these lines. One can construct Leontief input output tables from the make and use tables that are kept for the national income and product accounts (NIPAs). I would also like price indices for each industry at the level of the available NIPAs. There are many details and conventions that one should understand in working with such data, which I think I get muddled over when I've gone into details.

And much room exists for qualitative and historical work. One could draw on institutional economics in examining capital as power.

You can start to see scholars developing economics in this direction in the 1970s and early 1980s. I think of Donald Harris' Capital Accumulation and Income Distribution, Stephen Marglin's Growth, Distribution and Prices, Michio Morishima's Marx's Economics: A Dual Theory of Value and Growth, Luigi Pasinetti's Lectures on the Theory of Production, John Roemer's Analytical Foundations of Marxian Economic Theory, or Peter Skott's Conflict and Effective Demand in Economic Growth.

But most of the economists at the supposed best schools were uninterested or too craven to accept work along these lines as valid research programs. So much of academic economics is special pleading in bad faith for their paymasters among the plutocracy, as comes out in the news every once in a while. (Disclaimer: I own stock in Amazon and Apple.)

A Bowles Taxonomy For Economists

Katzner, Bowles, and Resnick on UMass Amherst

Shortly after about 32:30 minutes, Sam Bowles, to laughter, draws a Venn diagram on the board. This is a light talk, and Bowles is explicitly describing economics from his own experience at the University of Massachusetts at Amherst. Bowles places various economists in various subsets. I have varied the names a bit in my reproduction below.

Bowles' Taxonomy

I take the universe to be the set of all economists. Or, maybe, given Bowles includes John Rawls, it is a set of academics concerned with topics Bowles thinks economists should be concerned with. I take it that this taxonomy is not to apply to all time and space, but maybe only to academics from about 1970 to now. I explicitly added Kenneth Arrow, Milton Friedman, and Paul Samuelson as examples of economists that do not fall into any of the three numbered subsets. One might think Arrow extended the domain of economics to include voting, social choice, and health economics. So he illustrates my point about this taxonomy being time-bound. For all its originality, I do not think Samuelson's work on revealed preferences, the Heckscher-Ohlin-Samuelson model of international trade, or a model of overlapping generations, for example, can be said to have extended the domain of topics covered by economics.

Anyways, the three sets are those economists:

1. Who are critical of neoclassical economics.
2. Who want to extend the fields or topics to which economics applies.
3. Who are critical of capitalism.

Bowles talks about the intersection of the three sets as "us". I expanded that to label the intersection of four who I think exemplify radical political economics, as developed at UMass. In the talk, Bowles names more for some of the intersections, and, of course, the UMass economics department included more radicals.

By the way, I think the contrast about what they have to say in these talks at UMass about (Neo) Walrasian General Equilibrium Theory (GET) with what John Eatwell has to say of interest. Bowles and Resnick say that economists have now rid themselves of GET, but they have replaced it with "nothing". Mainstream economics, in some sense, have nothing to say nowadays about how the system works as a whole. And they continue to teach the old, outdated stuff to students.